I would def keep your door locked...forget robberies. What if a really dangerous person got in and hid, waiting for you to come home? It may sound like I'm paranoid, but it's something to think about. It's unlikely...but you know what I mean.
I say, get a key you can wear around your neck and keep a spare in your saddlebag. This way if you get separated from your bike, you can still get into your house from the key around your neck...and if THAT key goes flying b/c you fell off your bike, well, you always have the saddlebag key.